Year‐round weather alters nest‐provisioning rates in a migratory owl

Abstract As global temperatures and precipitation become more extreme, habitat specialists are at particular risk of being pushed past their environmental tolerance limits. Flammulated Owls (Psiloscops flammeolus) are small migratory owls that breed in temperate conifer forests of western North America. Their highly specialized nesting and foraging requirements make them indicators of ecosystem health. Using 17 years of nest observations, we investigated how annual weather patterns affected Flammulated Owl nesting and foraging behaviors during the breeding season. We used generalized linear models with a changepoint parameter to evaluate nest provisioning and nestling growth rates in years of extreme temperature and precipitation. We also evaluated how adult mass, division of labor, and productivity varied based on precipitation and temperature. Compared to wet and warm years, adults made more frequent prey deliveries to nestlings in dry and cold years, particularly early in the night and early in the season, and they experienced earlier changepoints in these years. We found a significant effect of temperature on the number of fledglings in broods, but weather did not affect other variables including productivity, nestling growth rates, adult masses, and division of labor. Our findings suggest that extreme annual weather patterns influence insect prey availability during the Flammulated Owl breeding season, forcing adults to work harder to provision for nests during dry and cold years. While productivity and nestling growth did not vary between years, these may incur a long‐term tradeoff in adult survival.

. Long-term studies of habitat specialists that elucidate changes in these organisms' behaviors can, therefore, provide valuable insights into the consequences of climate change for the overall ecosystem (Clavel et al., 2011;Donovan et al., 2002).
Flammulated Owls (Psiloscops flammeolus) have unique breeding requirements and life histories, making them indicators of environmental change in their forest ecosystems (Linkhart & Reynolds, 1997;McCallum, 1994;Van Woudenberg, 1999). Across their breeding range in western North America, these Neotropical migrants (Linkhart et al., 2016) are designated as a sensitive species by the United States Forest Service (McCallum, 1994) and a species of conservation concern by the United States Fish and Wildlife Service (USFWS) (2021), and species of special concern in Canada (COSEWIC, 2001). Flammulated Owls exhibit a life history strategy similar to large raptors by having high adult survival and a low annual reproductive rate (mean clutch size is 2.5 ± 0.1 eggs) with no evidence of renesting (Linkhart & Reynolds, 2006. Flammulated Owls are insectivorous and are most often associated with older forests containing yellow pine (subfamily Ponderosae) in the Rocky Mountains (breeding), Sierra Nevada Mountains (breeding), and Sierra Madre Mountains (breeding, resident, and wintering), where they primarily capture and feed on Lepidoptera in tree crowns and Coleoptera and Orthoptera on the ground (Marshall, 1957;Reynolds & Linkhart, 1992;Ross, 1969). Despite their reliance on small-bodied prey, Flammulated Owls are single-prey loaders, meaning they only carry one item of prey at a time. This allows for the number of prey items delivered to nests to be directly quantified by the number of visits an adult makes to the nest. It is also more energetically demanding for single-prey loaders (as opposed to multiple-prey loaders) to increase the number of prey they bring to the nest because they must make more foraging trips, rather than increase the number of prey captured per trip (Lessells & Stephens, 1983). Adult Flammulated Owls exhibit a strong division of labor, with females assuming all nest-caretaking roles and males acting as the principal foragers (Linkhart & McCallum, 2020).
We investigated the effects of annual precipitation and ambient air temperature (hereafter, temperature) on Flammulated Owl nestprovisioning rates, division of labor, body condition, nestling growth, and productivity using long-term nest observation data. Specifically, we used changepoint models to test how annual precipitation and temperature affect the rate of prey deliveries and division of labor (1) throughout the night and (2) over the course of the nestling period. We predicted that nest-provisioning rates would be higher in dry years than in wet years, and higher in cold years than in warm years, due to a lower abundance of high-quality prey, which would necessitate more frequent deliveries of the more relatively abundant low-quality prey. In cold years, prey delivery rates might also be higher because of increased nestling energy demands for maintaining homeothermy. We anticipated that prey delivery rates would drop off later in the night and later in the season in dry and cold years because of the increased foraging time required to meet nestling energy demands. We also predicted that adult females would increase their contributions to nest provisioning in dry and cold years to compensate for reduced male efficiency and higher nestling energy needs, which could lead to poor female body condition. Finally, we tested for an effect of precipitation and temperature on clutch size, brood size, the number of fledglings from each nest, and nestling growth rates. We predicted that both dry and cold years would result in lower overall productivity and slower nestling growth than wet and warm years due to the challenges adults face in meeting nestling, and their own, energy requirements. 17.0°C in July and −4.0°C in January, with snow often covering the ground from December through February (Frank et al., 2021;Ortega et al., 2014).

| Nest observation
We located all nests in the study area annually from 2004 to 2020 using methods developed by BDL (BDL, unpublished data;Linkhart & Reynolds, 2007;Reynolds & Linkhart, 1984). Briefly, we checked all tree cavities (excavated by picid woodpeckers) with diameters >4 cm using cameras mounted on telescopic poles. Cavities were usually checked weekly, beginning at the onset of laying (late May) until fledging (mid-July). We estimated nestling age by (1) backdating from the date of fledging (mean duration of nestling period was 23 days; Reynolds & Linkhart, 1987), (2) comparing camera photos showing plumage and morphometric development to photos of known-age nestlings, and/or (3) comparing lengths of primary feathers to primary lengths from known-age nestlings and fledglings (BDL, unpublished data).
To measure the rate of prey deliveries throughout the nestling period, we observed nests for at least one 15-min interval per week and recorded the total number of visits made to the nest by the attendant male or female. We varied the time of night to ensure a balance of early-and late-evening observations for each nest, and we recorded rates as the number of deliveries (as counts) per 15 min.
Following methods developed by Reynolds and Linkhart (1987), a prey delivery was attributed to the male if any one of the following criteria was met: (1) the female was known to be on the nest, (2) male vocalizations accompanied the delivery, or (3) the female was heard vocalizing off-nest while a second owl entered the cavity. A prey delivery was attributed to the female if any one of the opposing conditions was met, and deliveries made by an adult of unknown sex were not included in analysis. We omitted any intervals when nests were not observed for the full 15 min, and nest observations that occurred later than 90 min after sunset were not included in the analysis due to small sample sizes. Nonetheless, because prey delivery rates throughout the entire Flammulated Owl nestling period are maintained at their highest levels during this 90-min period (40%-80% higher than the rest of the night; Reynolds & Linkhart, 1987), we believe this window is most insightful, and sufficient, for detecting meaningful patterns on individual nights and over the full nestling period. We did not evaluate prey delivery rates in 2008, 2010, or 2016.
To estimate nest productivity, we recorded the clutch or brood size at each nest check. We estimated the number of fledglings by directly observing nestlings fledge from their nest, locating the fledglings after they had fledged, or observing nestlings within 1-3 days prior to their anticipated fledging. Brood sizes that were smaller than original clutch sizes were judged to be the result of unhatched eggs, partial or full nest predation during the incubation stage, or nest abandonment. Instances where the number of fledglings was smaller than brood size reflected partial or full predation during the nestling stage, siblicide, starvation, or nest abandonment. Nests with unknown fates were excluded from all analyses, but observations of failed nests were included if the observations preceded nest failure.

| Mass
We captured adult Flammulated Owls at nests or in a mist net with playback at least once, and in some cases multiple times, each breeding season. Individuals were massed (g) during each capture using a Pesola™ spring-loaded scale (accurate to 0.5 g). Multiple masses of the same adult within a season were uncommon but were recorded as separate observations if they occurred on different days, as were masses of the same individual in different years.
We included all adult masses in our analysis, even if the nest fate was unknown.
To weigh nestlings, we ascended nest trees during the day with a ladder or, if the tree was live, climbing hooks. All nestlings in a brood were removed from the nest and massed with a digital scale at least twice. Whenever possible, we captured owlets after observing them fledge and recorded their masses as the final day of the nestling period.

| Meteorological data
We downloaded hourly precipitation and temperature data for the Historical precipitation was totaled using the same start and end dates for each year from 1950 to 2000. Only 2 years of our study fell above the historical mean for total annual precipitation, and the mean annual precipitation from 2004 to 2020 (300.3 mm) was 71.8% of the mean annual precipitation from 1950 to 2000 (418.1 mm). We therefore, classified years falling above 71.8% of the historical mean as wet, and years falling below 71.8% were classified as dry (no years were equal to 71.8% of the historic mean).
Similarly, temperature was calculated by computing the mean daily minimum temperature between 1 June and 31 May for the historical period  and for our nest observation period. No years in our study fell within the 100% quartile of historical minimum temperatures, and the annual mean minimum temperature from 2004 to 2020 (−3.0°C) was 46.5% higher than the annual mean minimum temperature from 1950 to 2000 (−6.4°C). We therefore classified years between 2004 and 2020 as warm or cold based on whether they fell above or below 46.5% of the historical mean.

| Statistical analysis
Before considering precipitation and temperature as separate predictors, we tested for correlation between total yearly precipitation and average daily minimum temperatures using a Pearson's paired sample correlation test in the R stats package (R Core Team, 2021).
Precipitation and temperature were positively correlated (Pearson's correlation coefficient = .67, p < .001); we constructed one group of models for precipitation and a separate group for temperature.
Initially, we included precipitation and temperature as continuous numerical variables in all models. However, in addition to not seeing any initial effect of temperature and precipitation when treated as continuous, we were concerned that effects could be nonlinear due to extreme values. Consequently, we categorized the data into groups above and below the stated percentages of the historical means.
To determine how and when air temperature exerted the strongest effects on prey delivery rates, we ran Poisson GLMs using maximum likelihood estimation that tested for effects of three measures of air temperature during two different time periods. We considered (1) average daily air temperature, (2) minimum daily air temperature, and (3) maximum daily air temperature from (1) June-July (encompassing the nestling period) and (2) June-May (the 12 months preceding the initiation of breeding). We ultimately selected June-May average minimum daily air temperature, the model with the lowest Akaike information criterion (AIC) value, for subsequent analyses (Table A1 in Appendix 1).
To determine which time period to include in precipitation models, we considered total precipitation from (1) June-July (encompassing the nestling period), (2) June-May (the 12 months preceding the initiation of breeding), (3) January-June (capturing the major spring precipitation pulse), and (4) July-December (capturing the major summer precipitation pulse). The model using June-May precipitation as the predictor had the lowest AIC value and was, therefore, used for subsequent precipitation analyses.
To test for effects of precipitation and temperature on prey delivery rates, we used Poisson GLMs with a changepoint parameter.
Estimating changepoints was important because previous studies showed that Flammulated Owl prey delivery rates were nonlinear through time. Specifically, prey delivery rates increased for a short period immediately after sunset before dropping off later in the night; similarly, prey deliveries initially increased throughout the nestling stage before decreasing in the days preceding fledging (Reynolds & Linkhart, 1987). We adopted a Poisson-distributed Bayesian changepoint model to infer joined regression models for individual segments of a dataset using the R package mcp (Lindeløv, 2020).
Our final model formulation contained one changepoint and two segments, the first segment representing the early-evening or early-nestling stage, and the second segment representing the lateevening or late-nestling stage. The response variable for this logitlink model was the prey delivery rate, treated as count data (number of deliveries per 15 min); the predictor variable was time after sunset (min) for nightly models and nest age (days) for seasonal models. We used uninformative priors to estimate changepoints (uniform distribution between the minimum and maximum values of x and variance of 1000) and slopes (normally distributed around a mean of 0 and a variance of 1000) and assigned an intercept of 0 to our models because prey deliveries do not take place before sunset or before hatching. Each model was run separately for wet years, dry years, warm years, and cold years, with three chains with 20,000 iterations, burn-in of 4000, and thinning of 1. Model convergence was evaluated using Pearson residuals (plotted against fitted values), trace plots (ensuring convergence of all three chains), and R values (<1.1).
We evaluated the overlap of 95% credible intervals (CRIs) between variables to determine differences based on precipitation and temperature. If any of the 95% CRIs overlapped between models, we considered there to be no significant difference. The formula for these models was adapted from Lindeløv (2020): where Next, we evaluated whether precipitation and temperature influenced the extent of division of labor between males and females.
We initially used a Bayesian changepoint model with a beta distribution for the response variable to test the nightly and seasonal effects of climate on the proportion of total prey deliveries made by the female, but the CRIs for the changepoints were so broad (95% CRI ranged from 17 to 61 min for a single night and from 1 to 23 days for the nestling period) that we instead adopted a model without changepoints. After exploratory analysis, we constructed a Bayesian GLM with a beta distribution for the response variable to model the proportion of total prey deliveries attributable to the female throughout (1) a single night and (2) the breeding season for wet, dry, warm, and cold years. We used the package R2jags (Su & Yajima, 2021) to work with the models in R but connected with JAGS (Plummer, 2022) for the MCMC sampling. We used uninformative priors for the slopes and intercepts (uniform distributions with a mean of 0 and variance of 1000). Models ran on three chains with 10,000 iterations, burn-in of 1000, and thinning of 1. Like our changepoint model described above, model convergence was evaluated using residuals, trace plots, and R values (<1.1). We compared CRIs for wet and dry years and for warm and cold years; nonoverlapping 95% CRIs indicated significant differences in division of labor.
To assess the effects of precipitation and temperature on owlet growth, we used a Bayesian linear mixed effects model (Gaussian distribution) with a single changepoint, with nestling age as the fixed effect and mass as the response variable. To account for variation in growth rates across individuals, we included band number as a random effect (Cox et al., 2019). This allowed the changepoint and slopes (Segment 1) to vary by nestling, and the hyperparameter estimates of the changepoint and slopes took into account the number of measurements for each nestling. For this changepoint model, we included an intercept parameter because owlets have a nonzero mass at hatching. We used uninformative priors to estimate changepoints (uniform distribution between the minimum and maximum values of x and variance of 1000), slopes (normally distributed around a mean of 0 and a variance of 1000), and intercepts (same priors as slopes). Models ran on three chains with 4000 iterations, burn-in of 2000, and thinning of 1. Again, we ran the model for wet, dry, warm, and cold years and defined significance as nonoverlapping 95% CRIs between variables.
To test for an effect of climate on adult mass throughout the nestling period, we used a Bayesian linear model (Gaussian distribution) with mass as the response and Julian day as the predictor. This model was run separately for wet, dry, warm, and cold years. Analysis was also performed separately for males and females because of differences in nest-provisioning rates, and because only females exhibited brooding behavior (Reynolds & Linkhart, 1987). To account for the nonindependence of measurements from the same individual, we included band number as a random effect (Cox et al., 2019). This allowed the intercepts and slopes to vary by band number, and the hyperpa- Finally, we tested for an effect of precipitation and temperature on nest productivity. We used a Poisson GLM (fit in JAGS) to compare mean clutch size, brood size, and number of fledglings between wet and dry years and between warm and cold years. We used uninformative priors for the slopes and intercepts (uniform distributions with a mean of 0 and variance of 1000). Models ran on three chains with 20,000 iterations, burn-in of 4000, and thinning of 1.
Any 95% CRIs that did not overlap zero indicated significant effects of precipitation and temperature on productivity. We also compared the posterior distributions of the mean clutch size, brood size, and number of fledglings between wet and dry years and between warm and cold years and evaluated whether the CRIs overlapped between predictor variables.
All analyses were performed in R version 4.3.0, and we used the tidyverse and ggdist packages for data cleanup and visualization (Kay, 2021;R Core Team, 2023;Wickham et al., 2019).
Overall, prey delivery rates were higher in dry years than in wet years (Table 2). Throughout a single night, mean, maximum, and minimum rates were 17%, 24%, and 19% higher, respectively, in dry years than in wet years. Throughout the nestling period, mean prey delivery rates were 24% higher in dry years than in wet years, maximum rates were not significantly different, and minimum rates were identical (=1) for both dry and wet years.
Prey delivery rates were slightly higher overall in cold years than in warm years, although we noted more overlap of CRIs (Table 2).
Throughout a single night, mean and maximum rates were not significantly different, but minimum rates were 28% higher in dry years than in warm years. Throughout the nestling period, mean rates were 20% higher in dry years than in wet years, maximum rates were not significantly different, and minimums rates were identical (=1).
All prey delivery models estimated a single changepoint (Table 3; Figure 1). At the beginning of the night, deliveries increased at a higher rate in dry and cold years than in wet and warm years ( Figure A1 in Appendix 1). At the end of the night, deliveries decreased at similar rates between dry and wet years and between cold and warm years. The changepoint occurred 29% earlier in the night in dry years and 33% earlier in cold years than in wet and warm years, respectively.
At the beginning of the nestling period, prey deliveries increased at a higher rate in dry and cold years than in wet and warm years (Table 3; Figure A2 in Appendix 1). At the end of the nestling period, after the changepoints, rates continued to increase in dry and cold years but began to decrease in wet and warm years. The changepoints occurred 75% earlier in dry years and 80% earlier in cold years than in wet and warm years, respectively.

| Division of labor
Of 4078 total prey deliveries observed throughout the study, males accounted for more than three times as many as females (3090 vs.

deliveries, respectively).
Across all weather groups, the proportion of male prey deliveries remained constant over the course of a single night (Figure 2; Table A2 in Appendix 1). However, the proportion of female prey deliveries significantly increased with nestling age. The overall proportion of female prey deliveries did not significantly differ between wet and dry years or between warm and cold years.

| Mass
We recorded the mass of 229 males and 174 females throughout the study period, including 77 females (44%) and 97 females (56%) in wet versus dry years, respectively; 95 females (55%) and 79 females (45%) in warm versus cold years; 102 males (45%) and 127 males (55%) in wet versus dry years; and 119 males (52%) and 110 males (48%) in warm versus cold years. We did not detect a significant difference in adult mass between wet and dry or between warm and cold years (Figure 3; Table A3 in Appendix 1). Female mass decreased significantly throughout the nestling period in all years, but male mass remained constant.
We recorded the mass of 108 nestlings throughout the study period, including 45 nestlings (42%) and 63 nestlings (58%) in wet versus dry years, respectively, and 54 nestlings (50%) and 54 nestlings (40%) in warm versus cold years. On average, each nestling was weighed 10.2 times (range = 2-27). Nestling growth rates also did not differ based on weather. All models showed evidence for a single changepoint that occurred around day 16 in wet, dry, warm, and cold years ( Figure 4; Table A4 in Appendix 1). Slope estimates before and after the changepoint were not significantly different between wet and dry years or between warm and cold years. Intercept estimates were also highly overlapping, indicating similar owlet masses at hatching.

| Productivity
We did not detect a significant effect of precipitation on productivity. Warm years had a significant positive effect on the number of fledglings (n = 401 nests), but not on clutch (n = 319 nests) or brood (n = 381 nests) size (Table 4, Figure 5). All CRIs of the posterior mean overlapped between wet and dry years and between warm and cold years.

| DISCUSS ION
We found that the prey delivery rates were significantly higher in dry and cold years than in wet and warm years, both throughout a single night and throughout the nestling period. Further, prey deliveries increased at higher rates during the first part of the night and during the first part of the nestling period in dry and cold years. Taken together, these data suggest that in dry and cold years, either nestling energy demands were higher, high-quality prey were less abundant, or both. Several previous studies have reported negative effects of drought (as reviewed by Barnett & Facey, 2016) and cold temperatures (Frampton et al., 2000;Grüebler et al., 2008) on insect abundance. Therefore, it is unlikely that more frequent prey deliveries are TA B L E 1 Yearly summary of climate and nest productivity. detect any difference in owlet growth rates based on weather. We do not expect that lengthening the duration of prey delivery observation beyond 90 min would lead to different conclusions because our models showed delivery rates dropping off well before 60 min postsunset.
We do acknowledge, however, that predawn prey deliveries are also important for this species and were not evaluated in this study.
Later in the nestling period, prey delivery rates began to decrease in wet and warm years, while they continued to increase in dry and cold years. This elevated provisioning rate in cold years may indicate that late-stage nestlings need more energy to maintain homeothermy than in warm years, which coincides with when females are no longer brooding and can increase prey delivery rates. Despite the fact that tree cavities provide some insulation from temperature fluctuations, studies have shown that internal cavity temperatures decline significantly when the ambient air temperature drops below 16°C (Vierling et al., 2018), which is a common nightly occurrence at our high-elevation study site during the breeding season.
Precipitation in previous seasons can indirectly increase summer insect abundances by promoting plant growth, thus increasing food biomass for herbivorous insects and habitat for many other insects (Fay et al., 2003;Wu et al., 2011). The relationship between temperature and nest-provisioning rates is not clearly delimited, with some studies showing positive correlations between temperature and nest visitations (Brown, 1976;Finlay, 1976;Low et al., 2008) and others, including our study, showing the opposite (Barras et al., 2021;Grüebler et al., 2008;Schifferli et al., 2014). Since our study is unique in its focus on a single-prey loading species, further study is needed to determine the extent to which energetic costs of nest F I G U R E 1 Prey delivery (PD) rates throughout the night (top) and throughout the nestling period (bottom) differ based on precipitation (left) and temperature (right). Solid and dashed lines represent the fitted value computed using the mean of posteriors predicted from Bayesian changepoint models, and shaded ribbons represent the 95% credible interval of posteriors. Wet = green/solid, dry = yellow/ dashed, warm = red/dashed, cold = blue/ solid.

F I G U R E 2
Bayesian linear model (beta distribution) of the proportion of prey deliveries given by the female throughout the night (top) and throughout the nestling period (bottom). Solid and dashed lines represent the fitted value computed using the mean of posteriors, and shaded ribbons represent the 95% credible interval of posteriors. Wet = green/solid, dry = yellow/dashed, warm = red/dashed, cold = blue/solid.
provisioning in extreme temperatures are mediated by the extent of prey loading. Further study is also needed to determine effects of daily and seasonal temperature changes on nest-provisioning rates, thereby expanding on our focus on the full annual cycle to elucidate patterns over multiple temporal scales.
Adults worked harder in dry and cold years to deliver prey at higher rates, but the impact of this increased energy expenditure did not affect adult masses throughout the nestling period. Female mass decreased throughout the season, presumably because mass accumulated during laying and incubation was lost as females spent more time provisioning for the nest. Male mass, on the other hand, remained constant throughout the nestling period. These patterns in adult mass are common in other avian species that rely on a femaleonly incubation strategy (Cichon et al., 1999;Durant et al., 2004;Moreno, 1989). While our findings indicate adults did not incur short-term consequences of increased nest provisioning in dry and cold years, it is possible that Flammulated Owls will experience decreased adult survival if dry and cold years become more common.
Given the importance of adult survival in maintaining stable population growth, particularly in birds with low reproductive rates like Flammulated Owls (Clark & Martin, 2007;Ludwig et al., 2018), future studies should determine effects of extreme weather on adult survival in insectivorous birds.
The effects of precipitation and temperature on prey delivery rates did not appear to manifest in nestling growth. Our findings are consistent with many other studies of the effects of weather on avian nestling development (Dyrcz & Czyż, 2018;Gullett et al., 2015;Kruuk et al., 2015), but some effects on nestling development have been detected in cases where climate differences were extreme (Pérez et al., 2016) or masses were measured immediately after intense bouts of rainfall (Cox et al., 2019).
Beyond a positive effect of warm years on the number of fledglings, we found that weather did not significantly affect productivity.
The effects of precipitation and temperature on avian productivity varies in the literature, with most studies detecting no effect of these climate variables (Demay & Walters, 2019;Desante & Saracco, 2021;Gullett et al., 2015). However, some studies noted negative effects of heavy rainfall and low yearly temperatures on fledgling success (Ahola et al., 2009;Fisher et al., 2015). Unlike adult survival, nest success does not appear to be an important factor in determining population growth rates in species with small clutch sizes (Clark & Martin, 2007). formal analysis (supporting); funding acquisition (lead); investigation (lead); methodology (equal); project administration (lead); supervision (lead); visualization (supporting); writing -review and editing (equal).

ACK N OWLED G M ENTS
We thank the Colorado College students who conducted field work as part of the Flammulated Owl Research Crew, including K.

CO N FLI C T O F I NTE R E S T S TATE M E NT
The authors do not have any conflict of interest relevant to this project.

TA B L E A 4
Mean and 95% credible interval (CRI) of posterior estimates of changepoints, slopes, and intercepts for owlet mass changepoint models.
F I G U R E A 1 Distribution of posteriors predicted from Bayesian changepoint models of prey delivery rates throughout a single night. Black bars represent the mean (dot), 80% credible interval (thick bar), and 95% credible interval (thin bar). Darkest shades represent the 80% credible interval, medium shades represent the 95% credible interval, and lightest shades represent 100% of posterior estimates.

F I G U R E A 2
Distribution of posteriors predicted from Bayesian changepoint models of prey delivery rates throughout the nestling period. Black bars represent the mean (dot), 80% credible interval (thick bar), and 95% credible interval (thin bar). Darkest shades represent the 80% credible interval, medium shades represent the 95% credible interval, and lightest shades represent 100% of posterior estimates.